Theoretical descriptions of magnetic SANS are based on Brown's static equations of micromagnetics [1]}, which are a set of nonlinear partial differential equations for the magnetization along with complex boundary conditions on the sample's surface [2]}. Therefore, closed-form analytical results for the SANS cross section are restricted to special limiting cases such as the approach-to-saturation regime, where the governing equations can be linearized [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. Recently, we have carried out numerical micromagnetic computations to study the magnetic SANS cross section of microstructural-defect-free spherical nanoparticles during their transition from the single-domain to the multi-domain state [9]}, [10]}. The results for the magnetic SANS signal and correlation function have revealed pronounced differences as compared to the superspin model and provided guidance for the experimentalist to identify nonuniform vortex-type spin structures inside nanoparticles.
